PID Controllers for Time-Delay Systems

Cover......Page 1
Control Engineering \rSeries......Page 3
Title Page\r......Page 4
Publication Data\r......Page 5
Contents......Page 7
1.1 Introduction to Control......Page 14
1.2 The Magic of Integral Control\r......Page 16
1.3 PID Controllers......Page 19
1.4.1 The Ziegler-Nichols Step Response Method......Page 20
1.4.2 The Ziegler-Nichols Frequency Response Method......Page 22
1.4.3 PID Settings using the Internal Model Controller Design Technique......Page 24
1.4.4 Dominant Pole Design: The Cohen-Coon Method......Page 26
1.4.5 New Tuning Approaches......Page 27
1.5.1 Setpoint Limitation......Page 29
1.5.3 Conditional Integration......Page 30
1.7 Notes and References......Page 31
2.1 Introduction......Page 33
2.2 The Hermite-Biehler Theorem for Hurwitz Polynomials......Page 34
2.3 Generalizations of the Hermite-Biehler Theorem......Page 39
2.3.1 No Imaginary Axis Roots......Page 41
2.3.2 Roots Allowed on the Imaginary Axis Except at the Origin......Page 43
2.3.3 No Restriction on Root Locations......Page 47
2.4 Notes and References......Page 49
3.1 Introduction......Page 50
3.2 A Characterization of All Stabilizing Feedback Gains......Page 51
3.3 Computation of All Stabilizing PI Controllers......Page 62
3.4 Notes and References......Page 67
4.1 Introduction......Page 68
4.2 A Characterization of All Stabilizing PID Controllers......Page 69
4.3 PID Stabilization of Discrete-Time Plants......Page 78
4.4 Notes and References......Page 86
5.1 Introduction......Page 87
5.2 Characteristic Equations for Delay Systems......Page 88
5.3 Limitations of the Pade Approximation......Page 92
5.3.1 Using a First-Order Pade Approximation......Page 93
5.3.2 Using Higher-Order Pade Approximations......Page 95
5.4 The Hermite-Biehler Theorem for Quasi-Polynomials......Page 99
5.5 Applications to Control Theory......Page 102
5.6 Stability of Time-Delay Systems with a Single Delay......Page 109
5.7 Notes and References......Page 116
6.1 Introduction......Page 118
6.2 First-Order Systems with Time Delay......Page 119
6.2.1 Open-Loop Stable Plant......Page 121
6.2.2 Open-Loop Unstable Plant......Page 125
6.3 Second-Order Systems with Time Delay......Page 131
6.3.1 Open-Loop Stable Plant......Page 134
6.3.2 Open-Loop Unstable Plant......Page 138
6.4 Notes and References......Page 143
7.1 Introduction......Page 144
7.2 The PI Stabilization Problem......Page 145
7.3 Open-Loop Stable Plant......Page 146
7.4 Open-Loop Unstable Plant......Page 159
7.5 Notes and References......Page 168
8.1 Introduction......Page 169
8.2 The PID Stabilization Problem......Page 170
8.3 Open-Loop Stable Plant......Page 172
8.4 Open-Loop Unstable Plant......Page 187
8.5 Notes and References......Page 197
9.1 Introduction......Page 199
9.2 Robust Controller Design: Delay-Free Case......Page 200
9.2.1 Robust Stabilization Using a Constant Gain......Page 202
9.2.2 Robust Stabilization Using a PI Controller......Page 204
9.2.3 Robust Stabilization Using a PID Controller......Page 207
9.3 Robust Controller Design: Time-Delay Case......Page 211
9.3.1 Robust Stabilization Using a Constant Gain......Page 212
9.3.2 Robust Stabilization Using a PI Controller......Page 213
9.3.3 Robust Stabilization Using a PID Controller......Page 216
9.4.1 Determining k, T, and L from Experimental Data......Page 221
9.4.2 Algorithm for Computing the Largest Ball Inscribed Inside the PID Stabilizing Region......Page 222
9.5 Time Domain Performance Specifications......Page 225
9.6 Notes and References......Page 230
10.1 Introduction......Page 231
10.2 The Ziegler-Nichols Step Response Method......Page 232
10.3 The CHR Method......Page 237
10.4 The Cohen-Coon Method......Page 241
10.5 The IMC Design Technique......Page 245
10.7 Notes and References......Page 249
11.1 Introduction......Page 250
11.2 A Study of the Generalized Nyquist Criterion......Page 251
11.3 Problem Formulation and Solution Approach......Page 255
11.4 Stabilization Using a Constant Gain Controller......Page 257
11.5 Stabilization Using a PI Controller......Page 260
11.6 Stabilization Using a PID Controller......Page 263
11.7 Notes and References......Page 270
12.1 Introduction......Page 271
12.2 Algorithm for Linear Time-Invariant \rContinuous-Time Systems......Page 272
12.3 Discrete-Time Systems......Page 282
12.4 Algorithm for Continuous-Time First-Order Systems with Time Delay......Page 283
12.4.1 Open-Loop Stable Plant......Page 285
12.4.2 Open-Loop Unstable Plant......Page 286
12.5 Algorithms for PID Controller Design......Page 290
12.5.1 Complex PID Stabilization Algorithm......Page 291
12.5.2 Synthesis of Hoc PID Controllers......Page 293
12.5.3 PID Controller Design for Robust Performance......Page 297
12.5.4 PID Controller Design with Guaranteed Gain and Phase Margins......Page 299
12.6 Notes and References......Page 301
A.1 Preliminary Results......Page 302
A.2 Proof of Lemma 8.3......Page 306
A.3 Proof of Lemma 8.4......Page 307
A.4 Proof of Lemma 8.5......Page 308
B.1 Proof of Lemma 8.7......Page 311
B.2 Proof of Lemma 8.9......Page 312
C Detailed Analysis of Example 11.4......Page 316
References......Page 326
Index......Page 331